Universals and Particulars (1): A Distinction and a Problem

In this post I will attempt to clarify the universal-particular distinction in metaphysics. Then I will present an argument that this distinction is either absurd, or leads to an infinite regress. Later posts will attempt to answer this objection, explain more about universals and particulars, and relate this distinction to the difference between person and nature.

II.

A universal is a quality that can be had by more than one specific thing at a time. For example, there are many red objects. In fact, some red objects seem to have exactly the same shade of red. They exactly resemble each other with respect to the color red. In order to explain the fact that many objects exactly resemble each other in being red, some philosophers say that these objects share the same quality in common: redness. Because this redness can be had by more than one thing, it is not locally present in just one object; it is a universal.

A particular is a specific thing. For instance, “this red apple” is a different thing from “that other red apple”. Now pretend for a moment that two apples have all of the same features (universals) in common.[1] What makes them different? You cannot say “The apples are different because apple A is bigger than B” because we already clarified that there are no differences between them. It is tempting to say “they are different because A is in a different place than B” but this will not work. For in order to be in different places, the apples would already have to be different. It seems the best explanation is that “underneath” the shared features or universals of these two apples, there is a different specific thing—a particular. Apple A is a different particular from apple B. This distinction between shared universals and the particulars that have them can make sense of much of our experiences of difference and similarity.

III.

But there is a problem with this distinction. Consider our two apples. Both are red. That means both have the universal redness. At this point, we are making a claim about three things:

P1 (apple) – U1 (redness)
P2 (apple) – U1 (redness)

Each particular (P1, P2) apple has the same universal (U1) of redness. But now remember our argument for universals that was given above. When two things exactly resemble each other in some respect, that exact resemblance is a reason for thinking that they have the same feature in common. Obviously P1 and P2 share redness in common. But is it not also true that both of them share something else in common—namely “having a universal”? Surely we would say of P1 “P1 is red” and of P2 “P2 is red”. The fact that we would say the same thing about these two particulars matches up with the fact that there is something the same (redness) about these particulars. Would we not also say “P1 has a universal” and “P2 has a universal”? If so, it seems like we are introducing a new universal—“having”—into the mix. Now it seems that “having” is a quality shared by P1 and P2:

Thus it seems like if two particulars share the same first universal, then they must share a second universal (having).

IV.

As soon as we take “having” as a universal, we run into an infinite regress. Notice that P1 now has U2. But P2 also has U2. If both have U2, then they share in common “having U2”. So that requires another universal:

Naturally we need a U5 to explain how each particular has U4, and a U6, and a U7… and so an infinite regress begins.

V.

This prompts some philosophers to ditch the entire idea of a particular as something distinct from the properties of a thing. Remember that the standard way of understanding particulars is to take them as the bearers or possessors of properties; particulars are not properties. An alternative is to say that particulars are actually just groups of properties. If we cannot trace back from a finite number of properties to a particular that will bear properties, then why even bother with particulars at all? Why not just say an object is a chain of properties?

Perhaps this chain is finite in the number of properties that compose it. But if a philosopher wishes to maintain that “has” is a universal, then it seems based on the reasoning we considered in section IV. that he or she must be committed to an infinite number of properties as constitutive of an object.

One might object, “but what will distinguish one property-chain from another similar chain?” The defender of this cluster theory can reply that each cluster has a unique property all of its own that no other cluster has. Two clusters can be members of the same kind (two dog clusters for instance) and thus very similar. These dog clusters can have all of the same properties in common except one. It is this one property which a cluster can have to ground its uniqueness in contrast to all other clusters. What makes two otherwise identical dogs distinct? One of them has at least one property that the other lacks. This unique property can be called an individual essence, or haecceity. Perhaps this is sufficient to ground the distinctions between different objects.

V.

In my next post, I will argue that infinite regresses are neither helpful as explanations nor necessary in order to consistently maintain that universals exist.

3 Responses to “Universals and Particulars (1): A Distinction and a Problem”

Unfortunately, I lack sufficient formal training in philosophy to properly address the issues raised in your post. Fortunately, I make up for that lack with an abundance of brass temerity, so I’ll go ahead and try to address ’em anyways =).

The argument outlined in section IV seems to rely on the undesirability of an infinite regression in the following crucial way:

1) The possession of any universal by any particular implies an infinite chain of possessions of the “having” universal

2) Infinite chains are undesirable / illogical (this proposition is enthymic; what precedes is my best reconstruction of it)

3) Therefore no particular can possess a universal.

The use of proposition (2) is what particularly interests me. After all, infinite chains are of integral importance to mathematical analysis (i.e. the study of the field of real numbers), and their discovery and subsequent use by the mathematical community formed the basis for the development of the calculus, a branch of study with very real world applications.

Welcome to the blog. You do have *some* formal training in philosophy (THI counts for *something*, I should think–in fact, I’d say it counts for quite a bit) and your thoughts are quite reasonable regardless. So don’t feel out-of-place here.

To clarify about the argument of section IV., in that section the criticism is not that no particular can have a universal, but that if a particular has a universal, this requires an infinite regress of universals. In the next section, I consider three different options for a metaphysics (two explicitly, one implicitly): (1) ditch particulars (or at least ditch particulars understood as something outside of the category of property) and postulate a finite chain of universals, (2) ditch particulars and postulate an infinite chain of universals, or as a third option (3) keep particulars in our account of being, but say they need an infinite chain of universals in order to instantiate anything. I kind of ignore option 3 for two reasons. First, the particular viewpoint that I’m going to develop detailed arguments against in my next post is (2). Second, if particulars are postulated because of their explanatory fruitfulness in clarifying how it is possible for properties to be instantiated without an infinite regress of properties, then this seems unhelpful as an explanation. So I’m not assuming infinite regresses are bad, or that they preclude the possibility that particulars can have universals.

Regarding proposition 2 in your argument, I’d distinguish different kinds of infinities. Some infinities are infinite collections; I have no beef with those. Some infinities are infinite series; I find some of those troublesome. Infinities which are infinite series, but only have a kind of mental existence as representations, or a potential existence as not-yet realized series, do not seem problematic. Infinite series of actually existing things may be problematic (Craig’s Kalaam argument comes to mind). But I’m not even necessarily concerned with those. My concern will be with infinite series of entities which are postulated to ground the existence of an entity x. That’s where I think we run into problems. And I will explain why I think this in the next post.

Unless I am mistaken (which is not unlikely) the kinds of infinities required by mathematicians are not infinite explanatory sequences of the kind I’m concerned with. They are not attempts to answer the question “what grounds the existence of x?” where the entities which are postulated to ground x include “1” which is grounded in “2” which is grounded in “3” and so on “x–> 1–>, 2–>, 3–>, … ” How confused am I?